Battle was underway with me and partner A ready to defeat the door monster. I played a "Curse! Razzamafoo!" card on player B as I had a suspicion that he was about to interfere with the battle before it was over.

This card forces the player to discard their entire hand.

In response, he PLAYED his entire hand on our battle, raising the monster level to ridiculous amount. He claimed that he was playing those cards in response to the curse card I played, which everyone else at the table disagreed with.

The claim was that if I had played that curse on him outside of combat, he couldn't play the monster cards in response, but as it was in combat, he could. This seems like the incorrect way to resolve that card in my view.

However, with him being the only one with real Munchkin experience and the rest of us trying to get the hang of the game, we ended up leaving it at that and we had to run away from combat instead.

Seems to me that he could have played a counter-curse card in response, but not play cards into combat in response to a curse card that forced him to discard his entire hand.

To be very clear: You can't normally play cards in response to anything in Munchkin. It doesn't use a stack-based card play mechanic and once a card is played, it's resolved and then discarded or remains in play, depending on the card's purpose. If you're affected by a Curse, you resolve the Curse immediately. Only cards that say they cancel something can actually be played before resolving what's to be canceled, since that's the cancelling card's purpose.